Get Help

Turn on suggestions

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

- Community
- :
- PTC Mathcad
- :
- PTC Mathcad
- :
- Gough Stewart Platform

Options

- Subscribe to RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Printer Friendly Page

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-05-2018
11:42 AM

12-05-2018
11:42 AM

Gough Stewart Platform

Hi

I want to use a hexapod (gough stewart platform) in mechanical application.

The hexapode is formed with:

_ 1 base plate (ground)

_ 1 end effector (platform)

_ 6 leg (mechanical drive effector)

This system have 6 DoF for platform

For build this mechanical device, I need to calculate:

_ inverse kinematics : If i know the posture of platform, I find the leg lenght

(the posture is : 3 positions : dX,dY,dZ and 3 rotations : dRX,dRY,dRZ)

_ Leg Forces (traction-compression only generated in leg)

For start, i build the geometrical model, for this, i define a ground mark : O with coordinates 0,0,0

1)

I define the hinge point of base : Ai

2)

I define the hinge point of platform : Bi

3)

I define the C point is the géometrical center of platform

Now the leg are AiBi vector

I define a user mark

The user mark M ( 3 positions + 3 orientations) is define to mark O ( the origin of mark M is the point of interest)

For moving the platform, i define a new mark Mc from M

This mark is mark M augmented with strokes

And finally i calculate the AiBi vector, and i find the leg lenght.

I calculate AiBi at nominal position : not mouved platform

I calculate AiBi at mouved position

I find the stroke of effector (leg displacement)

Now I have a problem for Trajectory calculation

For know the stroke of effector, is necessary to compute leg lenght for trajectory.

The start point is define with stroke (in Mc)

dXmin dRXmin

dYmin dRYmin

dZmin dRZmin

The end point is

dXmax dRXmax

dYmax dRYmax

dZmax dRZmax

I use a lambda parameter for hash trajectory with 20 points for example

Now I find 20 group of position parameter.

I want to run my calculus for all position group, and finally i make a graph with leg lenght for position parameter group.

My calculus is right for calculate leg lenght for one position of platforme in 3D space.

But i can’t calculate for trajectory ( group of parameter ) and i can’t make a graph

I’am a mechanical men, not a software programmer (lol)

Do you can to help me ?

Labels:

30 REPLIES 30

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-05-2018
11:43 AM

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
04:27 AM

12-06-2018
04:27 AM

Re: Gough Stewart Platform

in first step. Perhaps i make 2 program

first:

Calculate all coordinates for trajectory points in 3D space

with stroke data entry

now

i make program wich calculate sucessive positions for all 6 parameters

__example for only dX translation:__

first position is dXmin

second position is dXmin+dXstep

... ( the step is (dXmax - dXmin) / lambda)

end with last position = dXmax

All position (dX,dY,dZ,dRX,dRY,dRZ) are must be concatenated in matrix Mc

Perhaps :

wrong ! it's don't work

I am bad in programming

please help me

I don't understand to correctly use mathcad program

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
05:07 AM

12-06-2018
05:07 AM

Re: Gough Stewart Platform

It's good with LucMeekes solution (give me it in another post)

i don't find it with program solutions

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
05:24 AM

12-06-2018
05:24 AM

Re: Gough Stewart Platform

But i have problem with LucMeekes solution's

Example

if the dY strokes = 0 (dYmin=0 , dYmax=0)

I don't have 0 in matrix ! because i divide by 0 in dY stroke calculus ! it,s wrong!

I want to give 0 in my matrix if stroke =0

maybe it's necessary to build programming solution for resolve this ?

i'm very sad, i'm alone in the dark with mathcad programming

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
05:28 AM

12-06-2018
05:28 AM

Re: Gough Stewart Platform

And if i want calculate position for one point in 3D space ! it's same divide by 0

example

dxmax= 30

dxmin= 30

error !

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
07:06 AM

12-06-2018
07:06 AM

Re: Gough Stewart Platform

I try it

example for stroke dX 0 to 5

but the first 0 is not correct

I don't understand why i have this first 0

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
07:47 AM

12-06-2018
07:47 AM

Re: Gough Stewart Platform

i find the problem

is ORIGIN Mathcad parameter

But it's not work correctly

and i need same number of point for each matrix

example

if dx have 20 rows

i need dy,dz,dRx,dRy,dRz have equal rows , here 20 rows

if, for example dy=0

i need 20 rows equal 0 in dy matrix ...

I'm very very bad in programming

And i need concatenated all in one matrix

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
08:58 AM

12-06-2018
08:58 AM

Re: Gough Stewart Platform

I try it

But i have another problem

it's OK for stroke = 0 at 0 positions

But it's wrong if the stroke =0 , nut the position = 5 for example

If dZmin= 5 and dZmax=5 the stroke =0 but the position of platform = 5

and finally i need my dZ matrix have :

5

5

5

...

for this last item, it's wrong, but i'm getting closer

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Notify Moderator

12-06-2018
09:23 AM

12-06-2018
09:23 AM

Re: Gough Stewart Platform

You know the coordinates in 3D cartesean space of the base of your six effectors (the A's in your diagram.)

If you know the posture of the platform then you know the coordinates of the B's, the ends of the effectors.

The length of each effector then is the magnitude of the vector |B-A|.

The challenge is going to be to restrict the platform to the range of acceptable effector lengths.

Top Tags